Uni-directional circularly polarized log periodic antenna



Dec. 3, 1963 D. G. BERRY 3,113,316

UNI-DIRECTIONAL CIRCULARLY POLARIZED LOG PERIODIC ANTENNA 6 Sheets-Sheet 1 Filed May 23, 1960 INVENTOR. BEER r DA W12 6.

Dec. 3, 1963 D. G. BERRY 3,113,

UNI-DIRECTIONAL CIRCULARLY POLARIZED LOG PERIODIC ANTENNA 6 Sheets-Sheet 2 Filed May 23, 1960 Mr E/ m! 5 6 m V my D. G. BERRY ONAL CIRCU Dec. 3, 1963 UNI-DIRECTI LARLY POLARIZED LOG PERIODIC ANTENNA 6 Sheets-Sheet 3 Filed May 23, 1960 INVENTOR. Dav/p 6. BERRY Dec. 3, 1963 D. e. BERRY 3,1 3,316

UNI-DIRECTIONAL CIRCULARLY POLARIZED LOG PERIODIC ANTENNA Filed May 23, 1960 6 Sheets-Sheet 4 FIE4 INVENTOR. DAV/2 6' BERRY Dec. 3, 1963 D. G. BERRY UNI-DIRECTIONAL CIRCU 3,113,316 LARLY POLARIZED LOG PERIODIC ANTENNA 6 Sheets-Sheet 5 Filed May 23, 1960 INVENTOR. DAVID 6. BE'RRY Dec. 3, 1963 D. G. BERRY UNI-DIRECTIONAL cmcu LARLY POLARIZED LOG PERIODIC ANTENNA Filed May 23, 1960 V 6 Sheets-Sheet 6 P IA-l INVENTOR. Dawn 6 BERRY BY M/% ATIWRNEYJ United States Patent 3,113,316 UNI-DERECTIONAL ClittClJLARLY POLARIZED LOG PERIODKC ANTENNA David G. Berry, Cedar Rapids, Iowa, assignor to Collins Radio Company, Cedar Rapids, lowa, a corporation of Iowa Filed May 23, 1960, .Ser. No. 31,068 13 Claims. ((11. 343-7925) This invention relates generally to antenna means for producing an elliptically polarized radiated field and in particular relates to logarithmically periodic antenna means for producing a uni-directional elliptically pol-arized beam.

There are in the prior art many different antenna systems capable of producing uni-directional elliptically polarized beams. The principal difiiculty with all of these prior art structures is that the shape or" the radiation beam varies considerably with changes in frequency. The most recent marked improvement in producing a unidirectional elliptically polarized beam which remains fairly constant over a large frequency range has been with the use of logarithmically periodic antenna elements (herein also referred to as log periodic antennas). The specific prior art configuration employing log periodic antennas will be described briefly later herein. First, however, to provide the reader with the proper background, a brief discussion of an individual log periodic antenna element will be given. Each element is generally triangular in shape, having a vertex and side elements defined by an angle a. More specifically, each element is comprised of at least two radial sections defined on a common side by the center line of the antenna element and on the other side by a radial line extending from the vertex at an angle a/Z. Each of these radial sections is comprised of a plurality of teeth or rods which are all similar to each other in shape but which become progressively larger and spaced progressively farthe apart as the distance from the vertex increases. The above relationship may be expressed by stating that the radial distance from the vertex to any point on any given tooth in a specific radial member bears a constant ratio 7 to the radial distance from the vertex to the corresponding point on the next adjacent tooth which is farther removed from the vertex than said given tooth. Thus 1- will always be less than unity. In the most general case, where each antenna element employs two radial members lying in the same plane, the teeth of one radial section are positioned opposite the gaps of the other radial memher.

The prior art antenna structure employing log periodic antennas to obtain a unidirectional elliptically polarized beam comprises four of these antenna elements consisting of two pairs of non-image, nonplanar antenna ele ments arranged in quadrature. The vertices of the four elements are located close together but not quite touching each other. To provide a rough mental image of the relative positions of the four antenna elements it might be said that the four elements form a pyramidal shaped structure with each of the four antenna elements forming one face of the pyramid. The ed es of the adjacent elements do not make contact with each other, being spaced apart a small distance.

It is to be noted that in order to provide an elliptically or circularly polarized (rotating) beam it is necessary to produce two fields which not only are space-oriented 90 apart, but are also time-phased 90 apart. In the prior art discussed immediately above such a rotating field is created in the following manner. The input signal is supplied across the two antenna elements of each diametrically positioned pair of antenna elements, i.e.,

one terminal of the transmission line carrying the input signal is connected to one of the antenna elements of each of the two pairs of diametrically positioned elements and the other transmission terminal is connected to the two remaining antenna elements. Such an arrangement establishes an electromagnetic field which is positioned apart in space. To provide a time phase difference of 90 it is necessary to stretch by a factor K=T the two antenna elements forming a diametrically positioned pair of antenna elements. It is to be noted that it is an inherent characteristic of log periodic antenna elements that a phase shift will be created in the radiated signal by stretching or shrinking the antenna element. Stretching or shrinking the antenna element is defined as changing all the radial dimensions of the antenna element by a constant factor K. In stretching a log periodic antenna element the relationship between the amount of phase shift and the constant factor K is expressed by the equation where A equals the phase advancement in radians. It will be apparent that if a phase shift of 90 is desired ()\=90), then K will equal 7 For a more detailed description of individual logarithmically periodic antenna elements and for a more detailed description of an existing antenna system employing log periodic antenna elements to produce an elliptically polarized beam, reference is made to United States patent application Serial No. $38,373, filed April 23, 1959, by Raymond H. Du Hamel and Fred R. Ore, entitled Elliptically Polarized Logarithmically Periodic Antenna, now Patent No. 3,013,268, United States patent application Serial No. 721,408, filed March 14, 1958, by Raymond H. Du Hamel and Fred R. Ore, entitled Logarithmically Periodic Antenna, now Patent No. 3,079,602, and United States patent application Serial No. 804,357, filed April 6, 1959, by Raymond 1H. Du Hamel and David G. Berry entitled Uni-Directional FrequencyJndependent Coplaner Antenna, now Patent No. 2,989,749, all of which are incorporated by reference as a part of this specification. Although the antenna system disclosed in application Serial No. 808,373 marks a definite improvernent over prior known antenna systems for producing elliptically polarized fields, there remains a troublesome amount of variation of field pattern over large frequency changes. This undesirable change in radiation pattern is believed to be due primarily to a lack of symmetry in the pyramidal arrangement of the antenna elements, i.e., each antenna element sees three other elements on one side thereof but no elements on the other side thereof.

An object of the present invention is to provide an antenna system employing logarithmically periodic antenna elements and capable of producing an elliptically polarized field in which the radiation pattern remains substantially constant over large changes in frequency.

Another object of the present invention is. to provide a relatively simple antenna structure for producing a unidirectional rotating radiated beam pattern wvhich remains substantially constant over large frequency changes.

A further purpose of the invention is the improvement generally of antenna systems for producing uni-directional elliptically shaped radiation patterns.

in accordance with the invention two booms of conductive material are positioned parallel with each other and relatively close together, and each boom has contained thereon two radial sections in such a manner that the total of four sections are positioned around the booms at 90 angular intervals. One of the two radial sections mounted on any given boom is stretched by a factor 1- with respect to the other radial section mounted thereon, t .us creating a time phase difference of 90 between the two radial sections. The two radial sections mounted on the outer boo-m are substantial mirror images of the two radial sections mounted on said given boom. The stretched radial sections are positioned physically 180 apart and the non-stretched radial sections are also positioned 180 apart, but normal to the stretched antenna sections, thus forming a structure, which from the end view resembles a sign with each of the four arms thereof representing a radial section. One terminal of the antenna radial transmission line is connected to one of the booms to supply energy to one stretched radial section and to one non-stretched radial section. The other terminal of the transmission line is connected to the other boom. In order to provideaiding electromagnetic fields in each of the diametrically positioned pairs of radial sections, the two radial sections forming each pair of diametrically opposed radial sections are [mirror images of each other.

In accordance with various embodiments of the invention the radial sections may be comprised of rectangularly shaped teeth, dipoles, triangularly shaped teeth or curvilinearly shaped teeth.

The above-mentioned and other objects and features of the invention will be more fully understood from the following detailed description thereof when read in conjunction with the drawings in which:

FIG. 1 shows a form of the invention employing a dipole arrangement;

FIG. 2 shows an embodiment of the invention employing solid rectangularly shaped teeth;

FIG. 3 shows another form of the invention employing rectangularly shaped teeth formed of wires;

FIG. 4 shows a form of the invention employing triangularly shaped teeth;

FIG. 5 shows a form of the invention showing curvilinearly shaped teeth;

FIG. 6 is a diagram showing, in some detail, means for supplying the two booms with the signal to be radiatcd, and further, shows a rough approximation of the current distribution along the individual dipole elements; and

FIG. 7 is a chart of exemplary antenna dimensions and current amplitudes.

Referring now more specifically to FIG. 1, the antenna structure is comprised of two booms 23 and 2); the boom 23 forming the outside conductor of a coaxial cable, the inner conductor thereof being represented by the dotted line 21. The inner conductor 21 is electrically connected to the boom 29 at point 25, the boom 29 having no inner conductor. Later herein the current distribution on the inner conductor 21 and the booms 23 and 29 will be discussed in some detail to show how the diametrically positioned pairs of radial sections produce aiding electromagnetic fields.

Supported rigidly on each of said booms 23 and 2% are two antenna radial sections. More specifically, on boom 23 there are mounted two radial sections 13 and 14, spaced 90 apart and on boom 29 there are mounted two radia sections 15 and in, spaced 90 apart. It will be observed that radial section 13 is positioned substantially diametrically opposite the radial section 16 and, further more, is an exact duplicate in shape to the section 16', i.e., it is a mirror image (with a small transverse displacement, however, due to the fact that booms 23 and 2? cannot lie along the same line). Similarly, radial section 14 is positioned diametrically opposite the radial section 15 and is a mirror image thereof (also with a small transverse displacement due to the fact that booms 23 and 29 cannot be coincident). In this specification it is to be understood that the phrases mirror image or substantial mirror image are modified to the extent of the small axial displacement caused by the use of two separate booms.

The radial dimensions of the radial sections 14 and 15 are denoted by the distances R and R The radial dimensions of the booms of the radial sections 13 and 116 are shown as KR and KR The radial section 14 feeds against the radial section 15 and the radial section 13 feeds against the radial section 16.

Referring now to FIG. 6, a more detailed discussion of the means for supplying the input signal to the various radial sections is as follows. As indicated hcreinbefore, the signal is brought in through a coaxial cable 20" which is affixed to the boom 23 by a suitable fixture 74. Also, it should be noted that in FIG. 6 only the two radial sections (14' and 15) are shown. The sections 13 and fro are omitted to simplify the diagram. It will be understood that the field produced by the sections 13 and 16 is at right angles with the field produced by sections 14' and 1d and, further, is out of phase therewith, timewise.

Assume that at any given instant of time there is conventional current flowing from right to left in FIG. 6 out of the inner conductor as indicated by arrow 21, and current flowing from left to right on the inner side of the outer conductor (boom 23). When this lastmentioned current reaches the end of the boom 23 it, having no place to go, will flow back along the outside surface of the boom 23 as indicated generally by the arrow 24. it is important to note that due to the inherent characteristics of the log periodic antenna there is virtually no end efiect involved, i.e., no reflection, almost none of the current will flow back (right to left) on the outside of the boom 23 beyond the last rod 26. Such phenomenon is due to the fact that as the current designed by the arrow 24- flows along the back of the outside boom 23 portions of it will be diverted out along the rods attached to the boom 23 such as rods 2-6, 27 and 28 and will be radiated into space. An additional portion of this current will be reflected back and forth be tween the rods with a portion being radiated into space with each reflection until it, too, is substantially completely radiated into space, leaving only a very small and negligible percentage of the current flowing beyond the last rod 26. a

The conventional current flowing in the inner conductor 31 flows in the direction of the arrow 32 at the aforementioned given instant of time being considered. Such current is the result of the cumulative currents in each of the individual dipoles, such as dipoles A through H. As in the case of the radial section .14 the current fiow along the boom 29 is reflected back and forth among the various dipole elements until substantially all of the current is radiated into space, thus creating a condition where there is no end effect, i.e., there is no current flow beyond (to the left of) dipole element 33.

In the foregoing discussion it is to be noted that it has perhaps been indicated that the current flow in each of the dipole elements is always of the same polarity at any given instant of time. Experimental evidence indicates, however, that this is not the case. The phase relationship between the currents in the individual dipole elements is a rather complex function, the theory thereof not being fully understood at the present time. The length of the vector, such as vectors 71, 72, and 73 is drawn to be proportional to the magnitude of the current in the nearest dipole. In the chart of FIG. 7 the relationship of phase and relative current amplitude of the various dipole elements A through H is shown. Further, in the chart of FIG. 7 the length of the dipole in wavelengths of the particular signal being used to gather the data of FIG. 7 is listed. It will be noted that the phase varies considerably. For example, the phase difference between the current on dipole A and the current on dipole E is 172. However, it can be stated definitely that whatever the details of the relationship of the currents in the various dipole elements are, the result of the structure shown in FIG. 6 is a radiated electromagnetic field polarizcd in the direction of the individual dipole elements. Further, such resultant radiated field has a definite time phase with respect to the radial sections 13 and 16, FIG. 1. Such time phase relationship is determined by the value of K, which has been defined hereinbefore as being equal to Since a time phase difference of 90 is desired K becomes equal to 1 Also, as can be seen from an examination of FIG. 1, and as has been discussed hereinbefore, the radial sections 13 and 16 are physically spaced 90 from the radial elements 14 and 15, thus completing the requirements for creating the rotating field identified generally by the reference character 41 of FIG. 1. More specifically, the radiated field 41 is created by the interaction of the fields designated by the vectors 42 and 4.30 which are space and time phased 90 apart.

Referring to FIG. 2, there is shown another form of invention employing radial sections comprised of solid rectangular shaped teeth extending from a solid triangular portion whose outer limits are defined by the angle [3. The radial sections 43 and 44 feed against one another to produce a radiated field in a direction indicated by the vector 45 and mirror-image radial sections 46 and 47 feed against one another to produce a radiated field polarized along the direction of vector 4%. (Vectors 45 and 48 represent instantaneous values of the field. The fields will, of course, be alternating ones.) The value of K in FIG. 2 is equal to T so that the two fields represented by the vectors 45 and 48 are time phased 90 apart. Since they are also space phased 90 apart a rotating circularly polarized field is obtained. It should be noted that by changing the value K to an either greater or lesser value the circularly polarized field can be changed into an elliptically polarized field with the major axis bisecting the acute angle formed by the vectors corresponding to vectors 45 and 48. i

in FIG. 2 the terms r and r(n+1) designate the radial dimensions of the inner sides of the teeth, i.e., the sides of the teeth nearest the apex of the structure; the apex being represented generally by the reference character 4-9. As discussed hereinbefore the ratio of r to r is equal to the ratio of R n+U to R which is equal to 1-.

Referring now to FIG. 3, the structure shown therein is comprised of four radial sections having rectangularly shaped teeth formed of Wire or rods. The various radial dimensions of the teeth are designated as R r R r KR, Kr KR and Kr l which have the same meaning in the structure of FIG. 3 as they do in the structure of FIG. 2. Radial sections 52 and 53 feed against each other and radial sections 5% and 51 feed against each other in a manner similar to diametrically positioned radial elements of FIGS. 1 and 2. A circularly polarized field 54 is produced thereby. It is to be noted that radial sections 52 and 53 are mirror images of each other and that radial sections 5% and 51 are mirror images of each other.

In FIG. 4 there is shown a structure also consisting of four radial sections 57, 58, 59, and 60 each radial section consisting of triangularly shaped teeth, such as teeth 55 and 56. As in the case of the structure of FIGS. 1, 2, and 3 diametrically positioned radial sections feed against each other. Thus, radial section 57 feeds against iirror-image radial section 58, and radial section E9 feeds against mirror-image radial section 66 The radial dimensions R R KR, and K.R measure the radial distances from the apex, such as apex '70, of the triangularly shaped teeth to the apex 61 of the over-all structure. Since K=T and, further, since the radial sections are arranged in quadrature, there is produced a circularly polarized field 62.

Referring now to FIG. 5, the structure shown therein consists of four radial sections designated generally by the reference characters 63, 64, 65, and 66. Radial sections 63 and 64 are mirror images of each other and feed against each other. Similarly, radial sections 65 and 66 are mirror images of each other and feed against each other. The notation of the various radial distances has the same meaning as defined hereinbefore with respect to FIGS. 1 through 4.

It is to be noted that in all of the structures of FIGS. 1 through 5 the diametrically positioned radial sections are mirror images of each other. Consequently, diametrically positioned radial sections produce aiding fields since the 180 phase difference caused by the fact that they are mirror images of each other is cancelled out by the fact that the signals applied to two positioned radial sections are 180 out of phase with each other.

It is to be noted that the forms of the invention herein shown and described are but preferred embodiments thereof and that various structural changes, including the size and shape of the teeth and the values of 7, a, and B and other parameters of the structure may be made without departing from the spirit or scope of the invention.

I claim:

1. An antenna having an apex and comprising four radial sections arranged substantially in quadrature, first boom means, second boom means positioned alongside said first boom means and parallel thereto, each of said radial sections being generally triangular in shape with the apex thereof generally coincident with the apex of said antenna and having one side thereof comprise a selected one of said first and second boom means and the outer side of each of said radial section being defined by a line forming an angle 66/2 with the selected boom means, first and second ones of said radial sections being mounted on said first boom means and spaced apart substantially third and fourth ones of said radial sections being mounted on said second boom means and spaced substantially 90 apart, said first and third radial sections being positioned substantially apart and being substantially mirror images of each other, said second and fourth radial sections being positioned substantially 180 apart and bein substantially mirror images of each other, each of said radial sections comprised of a plurality of teeth of conductive material, the radial distance from the apex of each of the triangularly shaped radial sections to a point on any given tooth thereon bearing a ratio ato the radial distance from said apex to the corresponding point on the adjacent tooth farther removed from said apex, the radial distances of said first and third radial sections measured from said apex bearing a ratio K to the corresponding radial distances of said second and fourth radial sections, transmission line means comprising a first conductor and a second conductor, said first conductor being connected to said first boom means and said second conductor means being connected to said second boom means.

2. An antenna in accordance with claim 1 in which K is equal to where A is the time phase shift desired between said first and third radial sections and said second and fourth radial sections.

3. An antenna in accordance teeth of each radial section consist of straight rods extending out from the boom to which the radial section is mounted, each of said rods being parallel with each other and having a length determined by a radial line extending from the apex of said antenna element and forming an angle (1/2 with said boom, the radial distance from said apex to any given rod having the said ratio '7' to the radial distance of the adjacent rod farther removed from said apex.

4. An antenna in accordance with claim 2 in Which with claim 2 in which the each of said radial sections comprises a solid triangularly shaped member having a first edge physically connected to said boom and having said second edge form an angle equal to {3/2 with said boom and having an apex nearly coincidental with the apex of said antenna, and in which said teeth are solid rectangularly shaped teeth extending from said outer edge of said member away from said boom, the outer edge of said teeth being defined by a radial line forming an angle 04/ 2 with the said boom, and corresponding sides of the teeth being parallel with each other.

5. An antenna in accordance with claim 2 in which said teeth of each of said radial sections extend outwardly from the boom to which the radial section is attached and are comprised of a rod bent to form rectangularly shaped teeth, the end edges of the teeth lying in a radial line extending from the apex of the antenna and forming an angle DL/Z with said boom and corresponding sides of each of said teeth with respect to said apex being parallel with respect to each other.

6. An antenna in accordance with claim 2 in which said teeth of each of said radial sections are triangular in shape and formed of a rod bent into said triangular shape, said teeth having one side thereof affixed to said boom and having the free apex lying in a radial line extending from the apex of said antenna and forming an angle 04/ 2 with the boom to which the radial section is attached, corresponding sides of the teeth sides of each tooth being parallel with respect to each other.

7. An antenna in accordance with claim 2 in which each of said radial sections comprises a solid triangularly shaped member having one edge afiixed to the boom to which the radial section is attached and having a second edge defined by a radial line extending from the apex of the antenna and forming an angle {3/ 2 with the associated boom, and in which said teeth are solid and curvilinear in shape, and extending outwardly from said solid triangularly shaped member away from said boom, the end edges of said teeth lying along a radial line extending from the apex of said antenna and forming an angle 2 with said boom, the inner and outer sides of each of said teeth defining concentric arcs having a center substantially coincidental with the apex of said antenna.

8. An antenna in accordance with claim 1 in which K is equal to where A is the time phase shift desired between said first and third radial sections and said second and fourth radial sections.

9. An antenna in accordance with claim 8 in which the teeth of each radial section consists of straight rods extending out from the boom to which the radial section is mounted, each of said rods being parallel with each other and having a length determined by a radial line extending from the apex of said antenna element and forming an angle a/ 2 with said boom, the radial distance from said apex to any given rod having the said ratio '7' to the radial distance of the adjacent rod farther removed from said apex.

10. An antenna in accordance with claim 8 in which each of said radial sections comprises a solid triangularly shaped member having a first edge physically connected to said boom and having said second edge form an angle equal to [3/ 2 with said boom and having an apex nearly coincidental with the apex of said antenna, and in which said teeth are solid rectangularly shaped teeth extending from said outer edge of said member away from said boom, the outer edge of said teeth being defined by a radial line forming an angle u/ 2 with the said boom, and corresponding sides of the teeth being parallel with each other.

11. An antenna in accordance with claim 8 in which said teeth of each of said radial sections extend outwardly from the boom to which the radial section is attached and are comprised of a rod bent to form rectangularly shaped teeth, the end edges of the teeth lying in a radial line extending from the apex of the antenna and forming an angle OL/Z with said boom, and corresponding sides of each of said teeth with respect to said apex being parallel with respect to each other.

12. An antenna in accordance With claim 8 in which said teeth of each of said radial sections are triangular in shape and formed of a rod bent into said triangular shape, said teeth having one side thereof affixed to said boom and having the free apex lying in a radial line extending from the apex of said antenna and forming an angle 0L/ 2 with the boom to which the radial section is attached, corresponding sides of the teeth sides'of each tooth being parallel with respect to each other.

13. An antenna in accordance with claim 8 in which each or said radial sections comprises a solid triangularly shaped member having one edge afiixed to the boom to which the radial section is attached and having a second edge defined by a radial line extending from the apex of the antenna and forming an angle 6/2 with the associated boom, and in which said teeth are solid and curvilinear in shape, and extending outwardly from said solid triangularly shaped member away from said boom, the end edges of said teeth lying along a radial line extending from the apex of said antenna and forming an angle 01/2 with said boom, the inner and outer sides of each of said teeth defining concentric arcs having a center substantially coincidental with the apex of said antenna.

References Cited in the file of this patent UNITED STATES PATENTS 1,988,434 Bohm Jan. 22, 1935 2,192,532 Katzin Mar. 5, 1940 2,298,449 Bailey Oct. 13, 1942 OTHER REFERENCES Pub. 1: Du Hamel and Ore, Logarithmically Periodic Antenna Designs, I.R.E. National Convention Record, Part I, Antennas and Propagation, Microwave Theory and Techniques, March 195 8, Received Sci. Lib. July '18, 1958, pages 139-151 (pages 147, 148, 149, relied on). 

1. AN ANTENNA HAVING AN APEX AND COMPRISING FOUR RADIAL SECTIONS ARRANGED SUBSTANTIALLY IN QUADRATURE, FIRST BOOM MEANS, SECOND BOOM MEANS POSITIONED ALONGSIDE SAID FIRST BOOM MEANS AND PARALLEL THERETO, EACH OF SAID RADIAL SECTIONS BEING GENERALLY TRIANGULAR IN SHAPE WITH THE APEX THEREOF GENERALLY COINCIDENT WITH THE APEX OF SAID ANTENNA AND HAVING ONE SIDE THEREOF COMPRISE A SELECTED ONE OF SAID FIRST AND SECOND BOOM MEANS AND THE OUTER SIDE OF EACH OF SAID RADIAL SECTION BEING DEFINED BY A LINE FORMING AN ANGLE A/2 WITH THE SELECTED BOOM MEANS, FIRST AND SECOND ONES OF SAID RADIAL SECTIONS BEING MOUNTED ON SAID FIRST BOOM MEANS AND SPACED APART SUBSTANTIALLY 90*, THIRD AND FOURTH ONES OF SAID RADIAL SECTIONS BEING MOUNTED ON SAID SECOND BOOM MEANS AND SPACED SUBSTANTIALLY 90* APART, SAID FIRST AND THIRD RADIAL SECTIONS BEING POSITIONED SUBSTANTIALLY 180* APART AND BEING SUBSTANTIALLY MIRROR IMAGES OF EACH OTHER, SAID SECOND AND FOURTH RADIAL SECTIONS BEING POSITIONED SUBSTANTIALLY 180* APART AND BEING SUBSTANTIALLY MIRROR IMAGES OF EACH OTHER, EACH OF SAID RADIAL SECTIONS COMPRISED OF A PLURALITY OF TEETH OF CONDUCTIVE MATERIAL, THE RADIAL DISTANCE FROM THE APEX OF EACH OF THE TRIANGULARLY SHAPED RADIAL SECTIONS TO A POINT ON ANY GIVEN TOOTH THEREON BEARING A RATIO $ TO THE RADIAL DISTANCE FROM SAID APEX TO THE CORRESPONDING POINT ON THE ADJACENT TOOTH FARTHER REMOVED FROM SAID APEX, THE RADIAL DISTANCES OF SAID FIRST AND THIRD RADIAL SECTIONS MEASURED FROM SAID APEX BEARING A RATIO K TO THE CORRESPONDING RADIAL DISTANCES OF SAID SECOND AND FOURTH RADIAL SECTIONS, TRANSMISSION LINE MEANS COMPRISING A FIRST CONDUCTOR AND A SECOND CONDUCTOR, SAID FIRST CONDUCTOR BEING CONNECTED TO SAID FIRST BOOM MEANS AND SAID SECOND CONDUCTOR MEANS BEING CONNECTED TO SAID SECOND BOOM MEANS. 